Nonparametric Estimation of Functional Dynamic Factor Model

Abstract

For many phenomena, data are collected on a large scale, resulting in high-dimensional and high-frequency data. In this context, functional data analysis (FDA) is attracting interest. FDA deals with data that are defined on an intrinsically infinite-dimensional space. These data are called functional data. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for functional data. In this paper, we study functional factor models for time-dependent functional data. We propose nonparametric estimators under stationary and nonstationary processes. We obtain estimators that consider the time-dependence property. Specifically, we use the information contained on the covariances at different lags. We show that the proposed estimators are consistent. Through Monte Carlo simulations, we find that our methodology outperforms the common estimators based on functional principal components. We also apply our methodology to monthly yield curves. In general, the suitable integration of time-dependent information improves the estimation of the latent factors.